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3.4 Trigonometry (A-level only)

3.4 Trigonometry (A-level only)

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Question 9
a.

Prove that

cosec⁡θcosec⁡θ−sin⁡θ≡sec⁡2θ\displaystyle \frac{\operatorname{cosec}\theta}{\operatorname{cosec}\theta - \sin\theta} \equiv \sec^2\thetacosecθ−sinθcosecθ​≡sec2θ

[4]
b.

Hence solve, for 0<θ<2π0 < \theta < 2\pi0<θ<2π, the equation

cosec⁡θcosec⁡θ−sin⁡θ=2tan⁡θ\displaystyle \frac{\operatorname{cosec}\theta}{\operatorname{cosec}\theta - \sin\theta} = 2\tan\thetacosecθ−sinθcosecθ​=2tanθ

Give your answers in terms of π\piπ.

[3]
Markscheme

3.4 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.4 Trigonometry (A-level only)

221 exam-style questions on CCEA A Level Maths 3.4 Trigonometry (A-level only), covering 3.4.1 Trigonometry (A-level only), 3.4.2 Trigonometry (A-level only), 3.4.3 Trigonometry (A-level only), 3.4.4 Trigonometry (A-level only), 3.4.5 Trigonometry (A-level only), 3.4.6 Trigonometry (A-level only), 3.4.7 Trigonometry (A-level only), and 3.4.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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